Suppose that the weather in a certain city is either sunny, cloudy, or rainy on a given day, and consider the following: 1) If it is sunny today there is a 70% chance it will be sunny tomorrow and a 30% chance that it will be cloudy. 2) If it is cloudy today there is a 40% chance it will be sunny tomorrow, a 40% chance that it will be cloudy, and a 20% chance that it will be rainy. 3) If it is rainy today there is a 40% chance it will be sunny tomorrow, a 30% chance that it will be cloudy, and a 30% chance that it will be rainy. Suppose the predicted weather for Friday is 55% sunny, 30% cloudy, and 15% rainy. What are the chances that Sunday will be rainy? Give your answer as a percentage and enter it into Ans. Do not approximate. Do not include the % symbol.

Assume that the fleet consists of 30 percent Lexus, 30 percent Infinity, and 40 percent automobiles. 80 percent of the Lexus cars, 60 percent of the Infinities, and 70 percent Mercedes have CD players. Use this information to answer the following questions. (1) What is the probability that a randomly selected car has a CD player? (2) What is the probability that a randomly selected car either is a Mercedes or has a CD pl.

1. Why is it so much more likely that some pair of people at a party will have the same birthday, than that someone at the party will have a birthday today?

18) Mordor is considering invading and conquering Gondor. Gondor has an alliance with Rohan, however it is unclear whether or not Rohan will maintain the alliance. Assume that there is a 30% probability that Rohan is a loyal ally that would help Gondor, and a 70% probability that they would abandon Gondor. Neither Gondor nor Mordor know whether Rohan is a loyal ally, although of course Rohan knows their own type. After nature chooses whether Rohan is a loyal ally, Gondor can either surrender or not. If Gondor surrenders, the game ends. If Gondor does not surrender, Mordor can invade or not. If Mordor does not invade, the game ends. If Mordor does invade, Rohan can either ride to Gondor's aid or not. If Rohan aids Gondor, the alliance will prevail. If they do not, Mordor will prevail. Gondor gets -80 utility for surrendering, -100 utility from being conquered, and 30 utility for winning the war, and 70 utility if Mordor does not invade. Mordor gets 100 utility if Gondor surrenders, 50…

12. An actuary is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of women. For each of the three factors, the probability is 0.1 that a woman in the population has only this risk factor (and no others). For any two of the three factors, the probability is 0.12 that she has exactly these two risk factors (but not the other). The probability that a woman has all three risk factors, given that she has A and B, is 1/3. Calculate the probability that a woman has none of the three risk factors, given that she does not have risk factor A. (A) 0.280 (B) 0.311 (C) 0.467 (D) 0.484 (E) 0.700 4

3. A gene can be either type A or type B, and it can be either dominant or recessive. Assume that P(A)=0.60. If the gene is type A, then there is a probability of 0.31 that it is dominant. There is also a probability of 0.22 that it is dominant given that a gene is type B. a. What is the probability that a gene is dominant? b. What is the probability that a gene is type A given that it is dominant?

21. *An actuary is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of women. For each of the three factors, the probability is 0.1 that a woman in the population has only this risk factor (and no others). For any two of the three factors, the probability is 0.12 that she has exactly these two risk factors (but not the other). The probability that a woman has all three risk factors, given that she has A and B, is 1/3. What is the probability that a woman has none of the three risk factors, given that she does not have risk factor A ? (0.467)

7. A drawer contains 6 black socks, 4 brown socks, and 2 green socks. Suppose one sock is drawn from the drawer and that it is equally likely that any one of the socks is drawn. Find the probabilities for each of the following: a. The sock is brown b. The sock is either black or green c. The sock is red d. The sock is not black

A. 40%B. 60%C. 20%D. 80%

Section 5.3   A computer software company receives hundreds of support calls each day. There are several common installation problems, call them A, B, C, and D. Several of these problems result in the same symptom, lock up after initiation. Suppose that the probability of a caller reporting the symptom lock up is 0.6 and the probability of a caller having problem A and a lock up is 0.5.   Step 1 of 2 :   Given that the caller reports a lock up, what is the probability that the cause is problem A? Round your answer to four decimal places, if necessary.   Step 2 of 2 : What is the probability that the cause of the malfunction is not problem A given that the caller is experiencing a lock up? Round your answer to four decimal places, if necessary.